Dr. Lincoln, I just want to say how much I've enjoyed your videos. I had plenty of Calculus, Physics and Chemistry in college, but your videos brought a lot of it back to me . You made them easy for folks to understand Cosmology.
Conservation of momentum fails to hold if Center-of-Mass frame is transformed by Lorentz Transformation to another inertial reference frame. vixra.org/abs/1802.0099 If velocities of both objects are transformed by Lorentz Transformation. Total momentum become totally different.
It's great to see the equations and I do enjoy your presentations. One catch about RUclips feed is that when you mention your next video I can't necessarily find it.
A neccesary explanation. Maybe (just "maybe") it had been more accurate to expose clearly that Einstein's two postulates were far from arbitrary. Actually, Einstein found off the way to reconcile the apparent discordance between two fundamental priinciples in Physics: the Galilean Principle of Relativity, that dictates the Laws of Physics are equal for any inertial observer, and the odd results of more modern Maxwell's Theory of Electromagnetism, that dictates the speed of light is equal for any inertial observer. "De facto", Einstein was able to understand , taking into account the Galilean principle, the speed of light was not a mere underrated phaenomon, but a Law of Physics in itself, so any inertial observer WOLD HAVE TO measure the same speed for a light beam. Then, he assumed the Lorentz-Fitzgerald factor (both thought it was a phenomenon worthy of a further "classic" explanation) as the mathematical expression for unifying two only apparent irreconcilable principles.
Equations are wonderful when a context is applied to the situation. Whilst there are many who desire nothing more than a journey through algebraic constructs there are others who have different learning mechanisms. My best suggestion is to keep a healthy balance
Boodysaspie I didn’t understand that either. I figured it out after shuffling numbers around on a piece of paper, but now I can’t remember how I did it :(
@Boodysaspie put everything on the left in brackets, then add a ^2. Then put a square root over that. Square everything inside. (I. e. apply the ^2) Then Multiply everything inside with 1/c^2 / 1/c^2. Now apply the outer squareroot to everything. I haven't tried it yet. So I might be wrongm Don't have paper nearby.
Boodysaspie cT’ / sqrt(c^2 - v^2) Move c to the denominator as 1/c. (Or multiply top and bottom by 1/c.) = T’ / [(1 /c) sqrt(c^2 - v^2) ] Pull 1/c into the sqrt by squaring it. = T’ / sqrt[(1 / c^2)(c^2 - v^2)] Multiply... = T’ / sqrt[(c^2 / c^2) - (v^2 / c^2)] The first term cancels. = T’ / sqrt ( 1 - (v^2 / c^2) ) Simplify the second term. = T’ / sqrt( 1 - (v /c)^2 )
The observed paths of light for stationary observer were 2 hypotenuse with velocity c. While in calculation, you used vertical distance of 2*W and sqrt(c^2 - v^2). I think, for stationary observer, inclined paths and their velocities shall be considered.
you make more sense than any physics video I have watched . you are one of the best physics teacher the internet, you make relativity sounds so easy I love your videos , and more math please !
This is very helpful. I don't have much of a math background so I'm starting from scratch but I've been trying to visualize what Einstein's theories mean and showing the math in an easy to understand manner is beneficial. I hope to ramp up to where I can eventually understand the more complex math.
'If one doesn't make Physics his/her everything, he/she will not succeed.' That's what my first Physics professor told us in the very first lecture. Fortunately, Physics is not everything, afterwards. Your lectures really revive my fascination for Physics!
As all of these vids, this is great. One consistency remark: in some other vids, like the one on time dilation, the moving object moves from right to left, so in the negative direction for the "standing" observer, while in this video, it moves from left to right, so in the positive direction for the standing observer.
Keep the equations in your Videos, that is how we learn, the more see the equations and how they are derived the more the equations will become a common tool that we will feel lost without!
Takes me back. We were never taught this explanation at school so I worked it out from first principles by exactly the same method. Ah fun times. Also taught me that no matter how complicated a maths equation looks you can rework it into something more basic albeit more long winded 😀
You weren't taught it in school because it's not true they make videos like this to hype up the work they do, photons only move in the direction there emitted, so only in a straight line, it doesn't have the momentum of the direction it's moving added to it.
Thank you Dr. Lincoln. I love this video as it helps to revise/learn relativity concepts. Indeed, I love equations, you do it in an understandable way, by anyone familiar with mathematics. Thank you!
I actually know your preferred explanation because you actually mention it in another video and yeah, it really makes way more sense when you look at it that way. When I saw it, my mind literally went 'Oh.. yes... that makes perfect sense.' It also explains why we keep saying 'time and space can be thought of as two kinds of direction' and why it works to treat time as a spacial dimension in these kinds of calculations.
Sir, I watched 6 lectures from Stanford by Lenny Suskind. After seeing the amount of computation needed to calculate all the tensor magic, I quit. These equations were a breath of fresh air. Moar please!
Oh yeah, those lectures are more for people who already have a bachelor's in physics. These videos are the place to be when taking your first steps into modern physics.
there is a nice tensor calculus series on youtube "tensor calculus and calculus of moving surfaces". its less physics based, but it spends much time on explaining the basic idea behind it, with some examples
Alexandru Gheorghe you must carry on bro.This happen to me too but after metric tensor equation just gonna fall out nice and slowly.Fermlab lecture would be more insightful(personal experience)☺
I loved this video, as all your other videos!!! Please feel free to put as many equations as needed. And please, keep them coming!!! Thank you very much.
Love the in-depth stuff; I'm a dunce at math so I (a) re-watch them, and (b) take your word for it. I won't cite a (c) because I now know c is the speed of light!
I found the equations challenging - I will need to sir down with a pen and paper. I was already aware, in general terms, that gamma was the ratio the hypotenuse and the adjacent. What I expected to see was the statement v = d / t. Then to say that as d increased and v stayed the same then t must change. However, you did something more precise and I will need to go over it again. For me it is a good challenge, please keep it coming.
loved it. i don't mind going in depth mathematically. i studied physics in college and i've learned to appreciate the intuition that only math can uncover :)
Perfect. Now things are falling into place for me. Even attempting some of my 'less curious' fellow seniors (70+) to understand this video. Another explanation I use is that travel through time-space is constant. The observer in the rail car traveled a greater distance that the stationary observer. Thus his time has to be less.
mrdsn189 Because the momentum is measured in relation to stationary/proper time, but removing gamma would be measuring it relative to moving time. The time being the time part of velocity (d/t.) If a person is walking on a moving train, the factor is negligible, so it seems just as easy to increase one's relative velocity, but near the speed of light it would be nearly impossible to move in any noticeable amount, because the amount of force required to accelerate your body would be astronomical. I apologize if I am incorrect in my understanding. Relativity can always be easily confusing.
because the "velocity" part of momentum contains "motion with respect to time", and for time you need to use what he called "stationary time" (the technical term people use is "proper time") From what he hinted at, it sounds like he's gonna expand on that next video btw.
Okay, think about it in this way. Now p=mv, which implies p is directly proportional to velocity and thus, inversely proportional to time taken. Now, time taken is different for different frame of references, so much be movement, right? If you consider looking at a special relativity test book, you would find this. Force, F is directly proportional to change in momentum and so to time taken. Momentum measured is different in different frame of references.
I'm not a theoretical physicist, but here's the thought experiment that helped me understand the increase in momentum (Spoiler Alert!): Imagine you're flying very fast in a space ship past a planet that's being hit by a meteor. Before impact, the meteor is flying in a direction perpendicular to your space ship, so that relativistic length contraction can be ignored. However time dilation does matter, meaning that someone observing the impact from the planet will observe the meteor's velocity to be larger than the observer from the space ship will see it. Now considering the strength of the explosion from the impact is the same for all observers, the slower velocity of the meteor as seen from the space ship must be compensated by a larger momentum of the meteor for the impact strength to make physical sense to both observers.
Universe Coder 1: We have to keep the speed of light the same for all observers, it's in the LOR. Universe Coder 2: But a stationary observer would see a longer path for the light than a moving one. Universe Coder 1: Hmmm, how about if we slow down time for the one moving? Universe Coder 2: .... WHAT? Do you realize the synchronization issues that would cause? Universe Coder 1: Okay, we'll quantize it, far easier to deal with then. Universe Coder 2: Ummm, that won't be compatible with our linear model at all. Universe Coder 1: Meh, don't worry, we'll cludge it.
I found seeing the math behind the phenomenon really assisted in understanding why distances and time measurements change as a consequence of spatial motion.
The lorentz factor is best understood as cd/sqr(c2-v2) where this is the hypotenuse, d is the distance light travels in the moving frame (inertial frame) perpendicular to the movement of the moving frame, and vd/sqr(c2-v2) is the distance traveled over the time that it takes for light to travel d. This is because c/sqr(c2-v2) is the Lorentz factor, simple algebra shows that 1/sqr(1-v2/c2) = c/sqr(c2-v2). It takes some thought, but put in the thought and everything becomes obvious. Factor out the ds and you will see that the Lorentz factor simply says that time and distance change by that amount as the frame moves at any speed, with the change increasing with velocity. Think some more and it becomes obvious that this must happen since c is the speed limit and a speed limit must exist.
Another great video. Math is good and your teaching ability is great also. Keep these videos coming!!!!! Also, how about a video on identical particles.
Maybe you can clarify but I always get lost at the moving train example, because the light is bouncing in a straight line relative to the inside of the train car I don't understand why the bystander sees it traversing more space and how we come to a hypotenuse. I am stuck on this hurdle and would greatly appreciate an answer that clicks in my head, thanks doc.
The bystander sees it traversing more space because he sees the light moving with the train, but the observer inside the train sees it as if it was stationary, but the speed of light is still the same for both observers.
@@blivion7203 is not it just a matter of perspective , the observer train just saw it as a straight libe because he was also moving with it. Light actually did travel a longer path as the outside observer sees it. Atleast in this example , i don't even think light would follow this that as photon wouldn't care about the speed of train , it wouos just travel up and down from the prespective of outside observer and to the left of the observer in train ( probably would not even hit the glass as glass would have moved further away).
Yes we love it , agree with you that this is incomplete or at least mesmerizing as gamma appears in many other equations like energy and it’s not clear how. ( In know energy and time are related , and illustration of that is the uncertainty principle , action etc)
Too light on the maths, and it's so simple it becomes boring for anyone who isn't a complete beginner. Too heavy on the maths, and it's essentially a university course. A middle-of-the-road approach is needed, and I think you've nailed it here. Two other channels which have also nailed it are viascience and PBS Space Time.
Another great video. I just wish I had a better grasp of math to understand the equations better. But the concept was very well presented. Thank you Dr. Lincoln.
I liked the video and the equations. I liked scrolling from one derivation to the next but I would find it even more helpful if I could see both equations at once instead of the bottom of the one and the top of the next. Seeing them both at the same time helps me see exactly what was done.
The units are needed to understand the equation. C is either 186k mph or 200 meters/ second W (width) is meters or miles & T is time in seconds or hours So T=2W/c is time=miles/mph or t=miles/(miles/hours) Expanding T = miles/(miles * 1/hours) T = hours * 1 miles cancels as miles/miles = 1 Leaving T = hours. Or metric sys T = meter/ meter per second T = meters /( meter * 1/seconds) T = ( meters/meters) * seconds Meters cancel as as anything divided by itself is one (1) Leaving T = seconds
Maybe I am missing something here. The observer outside the train sees light moving along a path that we may describe as the hypotenuse of the triangle, so what does this have to to with motion along the leg of the triangle perpendicular to the motion of the train? Motion of light along the hypotenuse is assumed to be at speed to be “c". Then c = hypotenuse/T(moving) Rewritten, hypotenuse = cT(moving) The length of the leg of the triangle along the axis of motion = vT(moving). The leg of the triangle perpendicular to the axis of motion is “w", and sicne it is perpendicular to the axis of motion, the observer outside the train does not observe and change in length. Then we get: Hypotenuse squared = perpendicular leg squared + parallel leg squared (cT(moving))^2 = w^2 + (vT(moving))^2 Solving for “w" we get w = cT(moving) times the square root of (1 - v²/c²). Ultimately. we get to the same place, but I think you cut corners, and I did not find that helpful.
It is possible to derive 2 contradictory time dilation equations. The first paragraph below describes the situation with Sally aiming a flashlight straight up and down so that Sally sees the light moving straight up and down and John is outside the spaceship and sees the light forming a triangle with the floor of the spaceship. The second paragraph describes Sally aiming a flashlight towards the left while the spaceship moves to the right. Now the situation is exactly reversed. Sally sees the light forming a triangle with the floor and John sees the light bouncing straight up and down. Sally is in a moving spaceship. John is outside the spaceship. Sally is moving to the right at .6c. The height of her spaceship is .8 light-seconds. If Sally has a light clock with the light bouncing straight up and down the light will make a 3-4-5 right triangle from the viewpoint of John. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived: delta T = delta T_o/((1-.6^2)^.5). So .8 seconds for Sally = 1 second for John. Now Sally has a light clock but this time she is holding a flashlight at an angle of 53.13 degrees above the horizontal and pointed to the left. Now the leftward movement of the light exactly matches the rightward movement of the spaceship from John's viewpoint. Now the light is bouncing straight up and down from the viewpoint of John and the light is making a 3-4-5 right triangle from viewpoint of Sally. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived: delta T_o = delta T/((1-.6^2)^.5). So 1 second for Sally = 0.8 seconds for John. The 2 equations are in direct contradiction to each other. Special relativity is falsified.
"Sally sees the light forming a triangle with the floor " No she doesn't it travels parallel to the floor as she sees it. "John sees the light bouncing straight up and down" No, he sees it travel parallel to the floor also. Maybe I have misunderstood what you are visulalising though.
From the perspective of something moving at the speed of light how fast would something else moving at the speed of light in the opposite direction be relative the first something ?
Great video! In one of the next videos, could you address the obvious conundrum that this video creates: If Jack is moving relative to Jill, Jill sees Jack's clock moving slower than her own. But Jill is also moving relative to Jack, so he will see her clock as moving more slowly than his own. So then, how is it possible for each of them to see the other's clock as moving more slowly? It doesn't look like it can have anything to do with the direction of the movement (toward or away).
ScienceNinjaDude Hopefully. I had a bad modern physics class in undergrad, and it failed to address the more interesting aspects of relativity or QM, instead focusing on asking questions in a way such that the answers were quick to grade.
The Lorentz transformation says something about velocities. How does it follow that we have time dilation or length contraction? One can manipulate velocities by any combination of scaling these factors.
There's this really cool principle that you can either use to derive the Lorentz gamma if you take it as a given, or if you already know how to calculate the Lorentz gamma, then you can derive this principle. Imagine you have a car that travels on a flat road. The car only has a steering wheel (no gas or break pedal), and it always travels at a constant speed. Let's give the speed a variable. How about (spoiler alert) C? Great. You can only change the direction, not the speed, of the car. Let's also assume that for some unknown reason, the car cannot travel southward at all. Now, let's say you don't know exactly what direction the car is traveling in, and you don't know if it's traveling northward at all. But you _can_ tell how quickly it's traveling eastward or westward. And you'd like to try and figure out if the car is traveling north at all, and if so, how quickly it's moving northward. Velocity vector. Pythagorean theorem. What's our triangle? The hypotenuse is the total speed of the car, which is always C. And one of the sides of the triangle is the eastward or westward speed. It doesn't matter which. Say we call west negative and east positive. Either way, since we're squaring it in the Pythagorean theorem, or solution for the other side (our northward speed) will be the same. Alright, but that's a two-dimensional plane. What does that have to do with the Lorentz gamma? That one's easy. You know how we have three spacial dimensions (3D, XYZ, length width height, etc.)? We'll just pretend we have one. And that total speed through 3D space will be one side of the triangle, and time will be the other side, and C will still be the hypotenuse. We're totally allowed to do that, by the way. You don't have to be able to visualize four dimensions in your head (I certainly can't) to do this. We'll just say that in addition to the three spacial dimensions, which are all perpendicular to each other (and thus have no cross influence), there is a fourth dimension, time, that is also perpendicular to those other three. Again, don't try to visualize it. Just accept the premise. We know that we can take a two-dimensional right triangle and rotate it however we'd like in 3D space. That rule doesn't change just because we added another dimension. And mathematically, you can just keep adding factors to the Pythagorean theorum and it still totally works. But again, we don't have to do that. We're just rotating the triangle in such a way that one of the sides of the triangle is lined up with (and the same length/magnitude as) our velocity vector, and the other side of the triangle is lined up with the (impossible to visualize IMO) time dimension. We take it on faith, for a moment, that everything is traveling through four-dimensional space-time at a constant rate of C, the speed of light. Therefore the length/magnitude/hypotenuse of our velocity vector never ever changes. All we can do is change the direction it points. Therefore if we know what our observed distance-per-time speed is (pretend that I remembered to say "observed" a dozen times earlier in this explanation) we know how quickly our observed clock speed is. And if you do the math (it just starts with C^2 = A^2 + B^2, where C is the speed of light, A is our observed speed through space, and B is our unknown observed time passage speed compared to "observed stationary clock") You get......... the Lorentz gamma formula! By the way, since light is always observed to travel at the speed of light (I'm starting to prefer the term "propagate" for light rather than "travel"), the Pythagorean theorem and Lorentz factor both tell us that the light itself is not observed to age, at all, ever. Its spacetime triangle would look like a line segment of length C, because one of the sides would have a length of C and the other side would have a length of zero.
Why is the beam of light which is moving towards and away from the mirror,also moving in the direction where the train is going? Its not, lets say a bullet, which has inherited the kinetic energy from the acceleration of the train,or is it?
Count me as another vote for these slightly more 'in depth' videos.
Seconded!
Thirded.
Count every one who have liked this comment
Just make a course on special relativity!
@@yashas9974 Definitely
Dr. Lincoln, I just want to say how much I've enjoyed your videos. I had plenty of Calculus, Physics and Chemistry in college, but your videos brought a lot of it back to me . You made them easy for folks to understand Cosmology.
I love the way you put humour in your physic video! ! It help me understand. Thank you professor
hes a doctor, not a professor
@@Psyadin2 soon?
Utter nonsense.
@@Gravadlax-ki7rh not when you're listening bro !
Brilliant. I want more and more rigorous topics to be taken up gradually.
I concur! Damn it Don Lincoln.....you need to get to WORK!!! .......................... Am I right?.........Just teasing Doctor.
collab with pbs spacetime maybe?
Listen to this guy
Couldn't agree more. I mean, for one thing there are all those 'delectable' enticements on the blackboard background...ha!
Conservation of momentum fails to hold if Center-of-Mass frame is transformed by Lorentz Transformation to another inertial reference frame.
vixra.org/abs/1802.0099
If velocities of both objects are transformed by Lorentz Transformation. Total momentum become totally different.
Your smile in the car is priceless. And as usual, a very clear and interesting video.
i think it had something to do with the car he was driving :)
THAT T-SHIRT!!!!!! Well done Doctor, well done
It's great to see the equations and I do enjoy your presentations. One catch about RUclips feed is that when you mention your next video I can't necessarily find it.
A neccesary explanation.
Maybe (just "maybe") it had been more accurate to expose clearly that Einstein's two postulates were far from arbitrary.
Actually, Einstein found off the way to reconcile the apparent discordance between two fundamental priinciples in Physics: the Galilean Principle of Relativity, that dictates the Laws of Physics are equal for any inertial observer, and the odd results of more modern Maxwell's Theory of Electromagnetism, that dictates the speed of light is equal for any inertial observer.
"De facto", Einstein was able to understand , taking into account the Galilean principle, the speed of light was not a mere underrated phaenomon, but a Law of Physics in itself, so any inertial observer WOLD HAVE TO measure the same speed for a light beam. Then, he assumed the Lorentz-Fitzgerald factor (both thought it was a phenomenon worthy of a further "classic" explanation) as the mathematical expression for unifying two only apparent irreconcilable principles.
This was a wonderful video, Dr. Lincoln. If possible, could we have even more videos which include the mathematical descriptions?
You are not only physicist
But also a great actor , comedian and teacher
This is the most adorable physics channel on RUclips.
Been struggling to understand time dilation for long. This video really helps me learn it piece by piece! Great work.
If you explain ecuations, then it's great...ecuations are scary/boring when you don't know where they come from but this...this is sweet!
Equations are wonderful when a context is applied to the situation. Whilst there are many who desire nothing more than a journey through algebraic constructs there are others who have different learning mechanisms. My best suggestion is to keep a healthy balance
It needs more equations, one can never have enough equations.
If there is anything I like more than cowbell it's equations.
As a mathematician, I wholeheartedly agree
Boodysaspie I didn’t understand that either. I figured it out after shuffling numbers around on a piece of paper, but now I can’t remember how I did it :(
@Boodysaspie put everything on the left in brackets, then add a ^2.
Then put a square root over that.
Square everything inside. (I. e. apply the ^2)
Then Multiply everything inside with 1/c^2 / 1/c^2.
Now apply the outer squareroot to everything.
I haven't tried it yet. So I might be wrongm Don't have paper nearby.
Boodysaspie
cT’ / sqrt(c^2 - v^2)
Move c to the denominator as 1/c. (Or multiply top and bottom by 1/c.)
= T’ / [(1 /c) sqrt(c^2 - v^2) ]
Pull 1/c into the sqrt by squaring it.
= T’ / sqrt[(1 / c^2)(c^2 - v^2)]
Multiply...
= T’ / sqrt[(c^2 / c^2) - (v^2 / c^2)]
The first term cancels.
= T’ / sqrt ( 1 - (v^2 / c^2) )
Simplify the second term.
= T’ / sqrt( 1 - (v /c)^2 )
The observed paths of light for stationary observer were 2 hypotenuse with velocity c. While in calculation, you used vertical distance of 2*W and sqrt(c^2 - v^2).
I think, for stationary observer, inclined paths and their velocities shall be considered.
wish you made video every week !!!
alexandre belinge me too !
you make more sense than any physics video I have watched . you are one of the best physics teacher the internet, you make relativity sounds so easy I love your videos , and more math please !
Excellently explained!! You are truly a gifted teacher! Keep up the great work doc!! Physics truly is everything!!
I like that slick way with the triangle you used to calculate time dilation. The typical way is much longer and more complicated! Bravo!
This is very helpful. I don't have much of a math background so I'm starting from scratch but I've been trying to visualize what Einstein's theories mean and showing the math in an easy to understand manner is beneficial.
I hope to ramp up to where I can eventually understand the more complex math.
'If one doesn't make Physics his/her everything, he/she will not succeed.'
That's what my first Physics professor told us in the very first lecture.
Fortunately, Physics is not everything, afterwards.
Your lectures really revive my fascination for Physics!
As all of these vids, this is great. One consistency remark: in some other vids, like the one on time dilation, the moving object moves from right to left, so in the negative direction for the "standing" observer, while in this video, it moves from left to right, so in the positive direction for the standing observer.
I felt that a frame of reference explanation was needed so asked for it, plus some equations, and I received. Thanks Santa!
We want more! More equations and episodes!! Way to go!!!
Dr. Lincoln,
Please keep doing what you are doing. I really love these videos. I can even handle the equations... mostly. :)
Thank you so much.
Love the equations! :)
Yay, nice, the equations! Love this channel!
Keep the equations in your Videos, that is how we learn, the more see the equations and how they are derived the more the equations will become a common tool that we will feel lost without!
3:38 I learned something I've wondered about for a long time.
Takes me back. We were never taught this explanation at school so I worked it out from first principles by exactly the same method. Ah fun times. Also taught me that no matter how complicated a maths equation looks you can rework it into something more basic albeit more long winded 😀
You weren't taught it in school because it's not true they make videos like this to hype up the work they do, photons only move in the direction there emitted, so only in a straight line, it doesn't have the momentum of the direction it's moving added to it.
Thank you Dr. Lincoln. I love this video as it helps to revise/learn relativity concepts. Indeed, I love equations, you do it in an understandable way, by anyone familiar with mathematics.
Thank you!
The easiest way to derive gamma (Lorentz factor). Thank you for the clarity.
I actually know your preferred explanation because you actually mention it in another video and yeah, it really makes way more sense when you look at it that way. When I saw it, my mind literally went 'Oh.. yes... that makes perfect sense.'
It also explains why we keep saying 'time and space can be thought of as two kinds of direction' and why it works to treat time as a spacial dimension in these kinds of calculations.
You are very good at explaining complicated concepts in a way that makes them easy to understand
Sir, I watched 6 lectures from Stanford by Lenny Suskind. After seeing the amount of computation needed to calculate all the tensor magic, I quit. These equations were a breath of fresh air. Moar please!
Dr. Susskind's "theoretical minimum" lectures are great!
Oh yeah, those lectures are more for people who already have a bachelor's in physics. These videos are the place to be when taking your first steps into modern physics.
Just another Susskind fan here :)
there is a nice tensor calculus series on youtube "tensor calculus and calculus of moving surfaces". its less physics based, but it spends much time on explaining the basic idea behind it, with some examples
Alexandru Gheorghe you must carry on bro.This happen to me too but after metric tensor equation just gonna fall out nice and slowly.Fermlab lecture would be more insightful(personal experience)☺
Just love your very simplistic approach in explaining a complex topic. Well done excellent!!
I'm glad we got more equations. I think longer videos will be also good...
I imagine those 45 'dislikers' being non-physicist scientists triggered by the big bang theory. Keep it up Dr Don!!
Love the lectures that give the brain time to absorb the concepts and information.
I loved this video, as all your other videos!!! Please feel free to put as many equations as needed. And please, keep them coming!!! Thank you very much.
That was really good and it is good to have equations. Thank you Dr Lincoln for your videos.
Don is the exact type of person I would expect to own a Corvette, and it made the explanation 10 times better
Love the in-depth stuff; I'm a dunce at math so I (a) re-watch them, and (b) take your word for it. I won't cite a (c) because I now know c is the speed of light!
I found the equations challenging - I will need to sir down with a pen and paper. I was already aware, in general terms, that gamma was the ratio the hypotenuse and the adjacent. What I expected to see was the statement v = d / t. Then to say that as d increased and v stayed the same then t must change. However, you did something more precise and I will need to go over it again. For me it is a good challenge, please keep it coming.
Thanks, Dr. Lincoln! Great video.... more equations!
I really enjoyed seeing the equations, please keep going this approach!
Fabulous level of explanation. Thank you Dr. Don, for everything!
wish you made video every day :)
there is no need to avoid equations too far. Equations are good way to expand your videos.
Keep on doing good work!
loved it. i don't mind going in depth mathematically. i studied physics in college and i've learned to appreciate the intuition that only math can uncover :)
Great series! Thanks for taking the time to make these. Very helpful.
Good stuff, Don. Looking forward to the next episode. The derivation here was very straight forward, but super useful.
This was perfect to help me get my head around the concept. I absolutely love your videos!
You are now my honourable teacher.
My god.. i have tried to understand time delation for so long and now I have got to really understand it. Thanks a lot Professor.♥️♥️
Equations are necessary to try to understand. Thank you.
Perfect. Now things are falling into place for me. Even attempting some of my 'less curious' fellow seniors (70+) to understand this video. Another explanation I use is that travel through time-space is constant. The observer in the rail car traveled a greater distance that the stationary observer. Thus his time has to be less.
I remember Al Bundy and Steve Rhodes in their convertible, singing along to Steppenwolf. What a charming video this is.
Thanks Dr. Lincoln. But why would the frame of reference matter for momentum though? Why does it need to be included in p=(m)(v)(gamma)?
mrdsn189 Because the momentum is measured in relation to stationary/proper time, but removing gamma would be measuring it relative to moving time. The time being the time part of velocity (d/t.)
If a person is walking on a moving train, the factor is negligible, so it seems just as easy to increase one's relative velocity, but near the speed of light it would be nearly impossible to move in any noticeable amount, because the amount of force required to accelerate your body would be astronomical.
I apologize if I am incorrect in my understanding. Relativity can always be easily confusing.
because the "velocity" part of momentum contains "motion with respect to time", and for time you need to use what he called "stationary time" (the technical term people use is "proper time")
From what he hinted at, it sounds like he's gonna expand on that next video btw.
Okay, think about it in this way. Now p=mv, which implies p is directly proportional to velocity and thus, inversely proportional to time taken. Now, time taken is different for different frame of references, so much be movement, right? If you consider looking at a special relativity test book, you would find this. Force, F is directly proportional to change in momentum and so to time taken. Momentum measured is different in different frame of references.
mrdsn189 Because momentum is a function of velocity which is a function of time and times are different for different observers
I'm not a theoretical physicist, but here's the thought experiment that helped me understand the increase in momentum (Spoiler Alert!): Imagine you're flying very fast in a space ship past a planet that's being hit by a meteor. Before impact, the meteor is flying in a direction perpendicular to your space ship, so that relativistic length contraction can be ignored. However time dilation does matter, meaning that someone observing the impact from the planet will observe the meteor's velocity to be larger than the observer from the space ship will see it.
Now considering the strength of the explosion from the impact is the same for all observers, the slower velocity of the meteor as seen from the space ship must be compensated by a larger momentum of the meteor for the impact strength to make physical sense to both observers.
Universe Coder 1: We have to keep the speed of light the same for all observers, it's in the LOR.
Universe Coder 2: But a stationary observer would see a longer path for the light than a moving one.
Universe Coder 1: Hmmm, how about if we slow down time for the one moving?
Universe Coder 2: .... WHAT? Do you realize the synchronization issues that would cause?
Universe Coder 1: Okay, we'll quantize it, far easier to deal with then.
Universe Coder 2: Ummm, that won't be compatible with our linear model at all.
Universe Coder 1: Meh, don't worry, we'll cludge it.
Love it. More equations please!
I found seeing the math behind the phenomenon really assisted in understanding why distances and time measurements change as a consequence of spatial motion.
The lorentz factor is best understood as cd/sqr(c2-v2) where this is the hypotenuse, d is the distance light travels in the moving frame (inertial frame) perpendicular to the movement of the moving frame, and vd/sqr(c2-v2) is the distance traveled over the time that it takes for light to travel d. This is because c/sqr(c2-v2) is the Lorentz factor, simple algebra shows that 1/sqr(1-v2/c2) = c/sqr(c2-v2). It takes some thought, but put in the thought and everything becomes obvious. Factor out the ds and you will see that the Lorentz factor simply says that time and distance change by that amount as the frame moves at any speed, with the change increasing with velocity. Think some more and it becomes obvious that this must happen since c is the speed limit and a speed limit must exist.
You are a very good teacher... it is very difficult for me but I hope I will understand at least the basics someday. Thanks
Another great video. Math is good and your teaching ability is great also. Keep these videos coming!!!!! Also, how about a video on identical particles.
Of course I loved it. I love all your videos, even the ones that take some time to soak in. Thanks for sharing your knowledge.
Definitely appreciated the equations, thank you. Now I can not wait to see what your favorite derivation is.
Maybe you can clarify but I always get lost at the moving train example, because the light is bouncing in a straight line relative to the inside of the train car I don't understand why the bystander sees it traversing more space and how we come to a hypotenuse. I am stuck on this hurdle and would greatly appreciate an answer that clicks in my head, thanks doc.
The bystander sees it traversing more space because he sees the light moving with the train, but the observer inside the train sees it as if it was stationary, but the speed of light is still the same for both observers.
@@blivion7203 is not it just a matter of perspective , the observer train just saw it as a straight libe because he was also moving with it. Light actually did travel a longer path as the outside observer sees it.
Atleast in this example , i don't even think light would follow this that as photon wouldn't care about the speed of train , it wouos just travel up and down from the prespective of outside observer and to the left of the observer in train ( probably would not even hit the glass as glass would have moved further away).
Much more interesting. Solving the equations allows me to both see and understand much more easily.
Such difficult things can be understood easily,thanks Dr . Lincoln
Yes we love it , agree with you that this is incomplete or at least mesmerizing as gamma appears in many other equations like energy and it’s not clear how. ( In know energy and time are related , and illustration of that is the uncertainty principle , action etc)
I love the mathematical explanation. Keep doing videos like this!
Thanks for the more in depth explanations. And yes... More equations along with your expert analysis of said equations. 😀
This is what tripped me up hard back in high school physics, it's just so weird compared to what was learned until then
Thank you for equations! It was brilliant. Thanks again!
Really nice video, hope next comes soon :D However, I think we all like to see this kind of approach to explaining equations, reeeally liked it
I like the videos with equations, more please!!
THANK YOU PROFESSOR LINCOLN...!!!
Too light on the maths, and it's so simple it becomes boring for anyone who isn't a complete beginner. Too heavy on the maths, and it's essentially a university course. A middle-of-the-road approach is needed, and I think you've nailed it here. Two other channels which have also nailed it are viascience and PBS Space Time.
Holy crap. Special relativity just made perfect sense. I need to lie down now. Mind blowing. Why did I not grok this 20 years ago?
Enjoyed this. I think I need to rewatch it but it's helping me get my head around this weird concept. I never really felt like I understood it.
Another great video. I just wish I had a better grasp of math to understand the equations better. But the concept was very well presented. Thank you Dr. Lincoln.
I liked the video and the equations. I liked scrolling from one derivation to the next but I would find it even more helpful if I could see both equations at once instead of the bottom of the one and the top of the next. Seeing them both at the same time helps me see exactly what was done.
The units are needed to understand the equation.
C is either 186k mph
or 200 meters/ second
W (width) is meters or miles
& T is time in seconds or hours
So
T=2W/c is time=miles/mph
or t=miles/(miles/hours)
Expanding
T = miles/(miles * 1/hours)
T = hours * 1
miles cancels as miles/miles = 1
Leaving T = hours.
Or metric sys
T = meter/ meter per second
T = meters /( meter * 1/seconds)
T = ( meters/meters) * seconds
Meters cancel as as anything divided by itself is one (1)
Leaving T = seconds
Could you put a link to the other videos you referred to in the description please.
Maybe I am missing something here. The observer outside the train sees light moving along a path that we may describe as the hypotenuse of the triangle, so what does this have to to with motion along the leg of the triangle perpendicular to the motion of the train?
Motion of light along the hypotenuse is assumed to be at speed to be “c".
Then c = hypotenuse/T(moving) Rewritten, hypotenuse = cT(moving)
The length of the leg of the triangle along the axis of motion = vT(moving).
The leg of the triangle perpendicular to the axis of motion is “w", and sicne it is perpendicular to the axis of motion, the observer outside the train does not observe and change in length.
Then we get:
Hypotenuse squared = perpendicular leg squared + parallel leg squared
(cT(moving))^2 = w^2 + (vT(moving))^2
Solving for “w" we get
w = cT(moving) times the square root of (1 - v²/c²).
Ultimately. we get to the same place, but I think you cut corners, and I did not find that helpful.
Thank you. Just discovered your channel and love it .
I AM STUCK IN A LOOP all his videos recommend another one of his videos and those videos recommend anotherrrrr !!!!!!!!!!!!!!!!!!
It is possible to derive 2 contradictory time dilation equations. The first paragraph below describes the situation with Sally aiming a flashlight straight up and down so that Sally sees the light moving straight up and down and John is outside the spaceship and sees the light forming a triangle with the floor of the spaceship. The second paragraph describes Sally aiming a flashlight towards the left while the spaceship moves to the right. Now the situation is exactly reversed. Sally sees the light forming a triangle with the floor and John sees the light bouncing straight up and down.
Sally is in a moving spaceship. John is outside the spaceship. Sally is moving to the right at .6c. The height of her spaceship is .8 light-seconds. If Sally has a light clock with the light bouncing straight up and down the light will make a 3-4-5 right triangle from the viewpoint of John. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived: delta T = delta T_o/((1-.6^2)^.5). So .8 seconds for Sally = 1 second for John.
Now Sally has a light clock but this time she is holding a flashlight at an angle of 53.13 degrees above the horizontal and pointed to the left. Now the leftward movement of the light exactly matches the rightward movement of the spaceship from John's viewpoint. Now the light is bouncing straight up and down from the viewpoint of John and the light is making a 3-4-5 right triangle from viewpoint of Sally. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived: delta T_o = delta T/((1-.6^2)^.5). So 1 second for Sally = 0.8 seconds for John. The 2 equations are in direct contradiction to each other.
Special relativity is falsified.
"Sally sees the light forming a triangle with the floor "
No she doesn't it travels parallel to the floor as she sees it.
"John sees the light bouncing straight up and down"
No, he sees it travel parallel to the floor also.
Maybe I have misunderstood what you are visulalising though.
Great video! It would be also nice to see a video about how Einstein used Lorentz transformation to develop a spacetime theory.
Relatividade. Recordar é viver. Obrigado. Dr.Lincoln
My father once told me that physic is not a vocation
, but for me physics is everything
I think he said vacation, and you must have mis-heard him. (*_*)
I was reading Feynman's lectures on the thing and I must say it's much easier to understand in a video.
From the perspective of something moving at the speed of light how fast would something else moving at the speed of light in the opposite direction be relative the first something ?
it would be moving at the same constant speed of light
More derivations & equations! These are great homeschool material
Great video! In one of the next videos, could you address the obvious conundrum that this video creates: If Jack is moving relative to Jill, Jill sees Jack's clock moving slower than her own. But Jill is also moving relative to Jack, so he will see her clock as moving more slowly than his own. So then, how is it possible for each of them to see the other's clock as moving more slowly? It doesn't look like it can have anything to do with the direction of the movement (toward or away).
ScienceNinjaDude Hopefully. I had a bad modern physics class in undergrad, and it failed to address the more interesting aspects of relativity or QM, instead focusing on asking questions in a way such that the answers were quick to grade.
The Lorentz transformation says something about velocities. How does it follow that we have time dilation or length contraction? One can manipulate velocities by any combination of scaling these factors.
There's this really cool principle that you can either use to derive the Lorentz gamma if you take it as a given, or if you already know how to calculate the Lorentz gamma, then you can derive this principle.
Imagine you have a car that travels on a flat road. The car only has a steering wheel (no gas or break pedal), and it always travels at a constant speed. Let's give the speed a variable. How about (spoiler alert) C? Great. You can only change the direction, not the speed, of the car. Let's also assume that for some unknown reason, the car cannot travel southward at all.
Now, let's say you don't know exactly what direction the car is traveling in, and you don't know if it's traveling northward at all. But you _can_ tell how quickly it's traveling eastward or westward. And you'd like to try and figure out if the car is traveling north at all, and if so, how quickly it's moving northward.
Velocity vector. Pythagorean theorem. What's our triangle? The hypotenuse is the total speed of the car, which is always C. And one of the sides of the triangle is the eastward or westward speed. It doesn't matter which. Say we call west negative and east positive. Either way, since we're squaring it in the Pythagorean theorem, or solution for the other side (our northward speed) will be the same.
Alright, but that's a two-dimensional plane. What does that have to do with the Lorentz gamma? That one's easy. You know how we have three spacial dimensions (3D, XYZ, length width height, etc.)? We'll just pretend we have one. And that total speed through 3D space will be one side of the triangle, and time will be the other side, and C will still be the hypotenuse. We're totally allowed to do that, by the way. You don't have to be able to visualize four dimensions in your head (I certainly can't) to do this. We'll just say that in addition to the three spacial dimensions, which are all perpendicular to each other (and thus have no cross influence), there is a fourth dimension, time, that is also perpendicular to those other three. Again, don't try to visualize it. Just accept the premise.
We know that we can take a two-dimensional right triangle and rotate it however we'd like in 3D space. That rule doesn't change just because we added another dimension. And mathematically, you can just keep adding factors to the Pythagorean theorum and it still totally works. But again, we don't have to do that. We're just rotating the triangle in such a way that one of the sides of the triangle is lined up with (and the same length/magnitude as) our velocity vector, and the other side of the triangle is lined up with the (impossible to visualize IMO) time dimension.
We take it on faith, for a moment, that everything is traveling through four-dimensional space-time at a constant rate of C, the speed of light. Therefore the length/magnitude/hypotenuse of our velocity vector never ever changes. All we can do is change the direction it points.
Therefore if we know what our observed distance-per-time speed is (pretend that I remembered to say "observed" a dozen times earlier in this explanation) we know how quickly our observed clock speed is. And if you do the math
(it just starts with C^2 = A^2 + B^2, where C is the speed of light, A is our observed speed through space, and B is our unknown observed time passage speed compared to "observed stationary clock")
You get......... the Lorentz gamma formula!
By the way, since light is always observed to travel at the speed of light (I'm starting to prefer the term "propagate" for light rather than "travel"), the Pythagorean theorem and Lorentz factor both tell us that the light itself is not observed to age, at all, ever. Its spacetime triangle would look like a line segment of length C, because one of the sides would have a length of C and the other side would have a length of zero.
Great explanation. Keep 'em coming. Thanks!
Why is the beam of light which is moving towards and away from the mirror,also moving in the direction where the train is going? Its not, lets say a bullet, which has inherited the kinetic energy from the acceleration of the train,or is it?